Radius of the circle which best approximates a curve at a given point
This article is about the general mathematical concept. For its optical applications, see Radius of curvature (optics).
In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof.[1][2][3]
^Weisstien, Eric. "Radius of Curvature". Wolfram Mathworld. Retrieved 15 August 2016.
^Kishan, Hari (2007). Differential Calculus. Atlantic Publishers & Dist. ISBN 9788126908202.
^Love, Clyde E.; Rainville, Earl D. (1962). Differential and Integral Calculus (Sixth ed.). New York: MacMillan.
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differential geometry, the radiusofcurvature, R, is the reciprocal of the curvature. For a curve, it equals the radiusof the circular arc which best...
Earth's radius involve the radiusofcurvature. A few definitions yield values outside the range between the polar radius and equatorial radius because...
that of a circle, which has a curvature equal to the reciprocal of its radius. Smaller circles bend more sharply, and hence have higher curvature. The...
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railways that cannot take the sharper curvature. For the handling of long freight trains, a minimum 574-foot (175.0 m) radius is preferred. The sharpest curves...
length of arc or chord. Curvature is usually measured in radiusofcurvature. A small circle can be easily laid out by just using radiusofcurvature, but...
When R = 0, the torus degenerates into a sphere with radius r. The greatest radiusofcurvatureof the toric lens surface, R + r, corresponds to the smallest...
life. The smaller the bend radius, the greater the material flexibility (as the radiusofcurvature decreases, the curvature increases). The diagram to...
kinematics of curved motion it is known that an object moving at tangential speed v along a path with radiusofcurvature r accelerates toward the center of curvature...
Leibniz. The center and radiusof the osculating circle at a given point are called center ofcurvature and radiusofcurvatureof the curve at that point...
normal plane. Profile radiusofcurvature is the radiusofcurvatureof a tooth profile, usually at the pitch point or a point of contact. It varies continuously...
capillary, the radiusofcurvature will also increase, creating a flatter interface. (Note: This is not to say that larger radii ofcurvature result in more...
in Book 1 of Philosophiæ Naturalis Principia Mathematica as Proposition 30. The focal length of a parabola is half of its radiusofcurvature at its vertex...
portion of it. A sphere has a single radiusofcurvature, which is simply the radiusof the sphere. More complex surfaces have radii ofcurvature that vary...
surfaces. The reciprocal of the radiusofcurvature is called the curvature. A flat surface has zero curvature, and its radiusofcurvature is infinite. If d...
the assumption that the lens is relatively thin.) The radiusofcurvature R {\displaystyle R} of the surface can be obtained from the optical power given...
negative radiusofcurvature, so f = − R 2 , {\displaystyle f=-{R \over 2},} where R is the radiusofcurvatureof the mirror's surface. See Radiusof curvature...
ofcurvature so obtained would be related to the equatorial radius and the polar radius, respectively a and b (see: Earth polar and equatorial radius...
geometry, the center ofcurvatureof a curve is found at a point that is at a distance from the curve equal to the radiusofcurvature lying on the normal...
curve whose curvature changes linearly with its curve length (the curvatureof a circular curve is equal to the reciprocal of the radius). This curve...
and radiusofcurvature R, separated by some distance d. For the purposes of ray tracing, this is equivalent to a series of identical thin lenses of focal...
at the plane z along the beam, w0 = w(0) is the waist radius, R(z) is the radiusofcurvatureof the beam's wavefronts at z, and ψ(z) is the Gouy phase...
susceptible to distortion. The radiusofcurvatureof a curved display is the radius that a circle would have if it had the same curvature as the display. This...